The Tengiz and Korolev fields are carbonate reservoirs in western Kazakhstan with substantial oil production, in part fed from naturally formed nonmatrix networks (here defined as fractures, karst caverns, and smaller karst features). Borehole image (BHI) logs are the primary tool for identifying and documenting fractures and karst caverns at wells due to their substantial reservoir coverage; however, core data sets, although much more spatially limited, provide critical ground truth for fracture presence and other characteristics. Using established approaches, rigorous calibration of BHI-based fracture picks with core reveals that a considerable percentage of BHI picks did not represent natural fractures (false picks), and, furthermore, some obvious natural fractures observed in core were not clearly detectable in BHI logs (missed fractures). Mining our calibration data, we found relationships with BHI pick attributes (e.g., sinusoid continuity) and geologic setting (e.g., environment of deposition) that allowed development of corrective measures to account for false picks and missed fractures away from core control, as well as guidelines to predict fracture openness and genetic fracture type. Corrected BHI fracture picks, when integrated with dynamic data, karst caverns interpreted from logs, and fracture openness relationships from core, allow for multiple fracture–karst density realizations at wells to capture a range of reservoir scenarios for static modeling. This study highlights the value of core in addressing the limitations and improving the accuracy of log-based fracture characterization and can be applied to other fields and reservoir settings.